If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is \(A\cup B\)?
Answer and explanation
Correct answer: \(\{1,2,3,4\}\)
The union \(A\cup B\) contains every distinct element found in either \(A\) or \(B\). Set \(A\) contributes 1, 2, and 3; set \(B\) contributes 3 and 4. Since 3 is common, it is listed only once, giving \(A\cup B=\{1,2,3,4\}\). The universal set \(U\) provides the surrounding context but does not mean that all elements of \(U\) belong to the union.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,3,4\}\)
Why is this the correct answer?
The union \(A\cup B\) contains every distinct element found in either \(A\) or \(B\). Set \(A\) contributes 1, 2, and 3; set \(B\) contributes 3 and 4. Since 3 is common, it is listed only once, giving \(A\cup B=\{1,2,3,4\}\). The universal set \(U\) provides the surrounding context but does not mean that all elements of \(U\) belong to the union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
